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For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter,…
When solving propositional logic satisfiability (specifically 3SAT) using quantum annealing, we analyze the effect the difficulty of different instances of the problem has on the quality of the answer returned by the quantum annealer. A…
Contextuality is a fundamental non-classical property of quantum theory, which has recently been proven to be a key resource for achieving quantum speed-ups in some leading models of quantum computation. However, which of the forms of…
In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form. Specifically, we consider the use of…
Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for…
Currently, existing quantum annealers have proven themselves as viable technology for the first practical applications in the noisy-intermediate-scale-quantum era. However, to fully exploit their capabilities, a comprehensive…
Recent theoretical and experimental studies have suggested that quantum Monte Carlo (QMC) simulation can behave similarly to quantum annealing (QA). The theoretical analysis was based on calculating transition rates between local minima, in…
It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement-based quantum computing…
A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a…
The paper deals with a full annealing process, for example for a metal alloy perturbed by some fractional noise caused by conditions in furnace such as initial temperature, initial structure of material itsel. The energy of the heating…
Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare…
An important challenge in superconducting quantum computing is the need to physically couple many devices using quasi-two-dimensional fabrication processes. Recent advances in the design and fabrication of quantum annealing processors have…
Quantum annealing is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. Quantum annealing in the transverse field Ising model, implemented on D-Wave…
There are many factors that influence the design of quantum annealing processing units. Here we address the issue of improving quantum annealing processing unit designs from the point of view of the critical behavior of spin glasses. It has…
Current generation quantum annealers have already proven to be successful problem-solvers. Yet, quantum annealing is still very much in its infancy, with suboptimal applicability. For instance, to date it is still an open question which…
Optimal parameter setting for applications problems embedded into hardware graphs is key to practical quantum annealers (QA). Embedding chains typically crop up as harmful Griffiths phases, but can be used as a resource as we show here: to…
We investigate the properties of quantum annealing applied to the random field Ising model in one, two and three dimensions. The decay rate of the residual energy, defined as the energy excess from the ground state, is find to be…
In a typical quantum annealing protocol, the system starts with a transverse field Hamiltonian which is gradually turned off and replaced by a longitudinal Ising Hamiltonian. The ground state of the Ising Hamiltonian encodes the solution to…
We introduce transverse ferromagnetic interactions, in addition to a simple transverse field, to quantum annealing of the random-field Ising model to accelerate convergence toward the target ground state. The conventional approach using…
Reverse annealing is a relatively new variant of quantum annealing, in which one starts from a classical state and increases and then decreases the amplitude of the transverse field, in the hope of finding a better classical state than the…